Moving Source, Observer at Rest, derivation for Doppler effect

In summary, the question asks whether the equation assumes that ##\frac{v}{f} ≥ \frac{v_S}{f}## in order for the wavelength to not be negative. The response clarifies that the object would be moving faster than the sound speed, indicating a supersonic speed which is a different physical regime.
  • #1
ChiralSuperfields
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Homework Statement
Please see below
Relevant Equations
Please see below
For this,
1685661674611.png

Does someone please know whether they assume for the equation highlighted that ##\frac{v}{f} ≥ \frac{v_S}{f}## since otherwise the wavelength would be negative (which I assume is impossible)?

Many thanks!
 
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  • #2
ChiralSuperfields said:
Homework Statement: Please see below
Relevant Equations: Please see below

For this,
View attachment 327342
Does someone please know whether they assume for the equation highlighted that ##\frac{v}{f} ≥ \frac{v_S}{f}## since otherwise the wavelength would be negative (which I assume is impossible)?

Many thanks!
The object would be moving faster than the sound speed; i.e., supersonic which is a different physical regime.
 
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Likes ChiralSuperfields
  • #3
Frabjous said:
The object would be moving faster than the sound speed; i.e., supersonic which is a different physical regime.
Thank you for your reply @Frabjous!
 

1. What is the Doppler effect?

The Doppler effect is the change in frequency or wavelength of a wave as perceived by an observer when the source of the wave is moving relative to the observer. This effect is commonly observed with sound waves, where the pitch of a sound appears higher when the source is approaching and lower when the source is moving away.

2. How is the Doppler effect derived for a moving source and observer at rest?

The Doppler effect can be derived using the principle of superposition, where the total wave observed at a point is the sum of all individual waves from each point on the source. By considering the relative motion of the source and observer, the change in frequency can be determined using the equation: Δf/f = v/c, where Δf is the change in frequency, f is the original frequency, v is the velocity of the source, and c is the speed of the wave.

3. What is the difference between the Doppler effect for sound waves and light waves?

The Doppler effect for sound waves is based on the relative motion of the source and observer, while the Doppler effect for light waves is based on the relative motion of the source and observer as well as the medium through which the wave is traveling. This is because sound waves require a medium to travel, while light waves can travel through a vacuum.

4. How does the Doppler effect impact everyday life?

The Doppler effect has many practical applications in everyday life. It is used in radar technology to measure the speed of moving objects, such as cars or airplanes. It is also used in medical imaging techniques, such as ultrasound, to detect the movement of blood or organs in the body. Additionally, the Doppler effect is used in astronomy to measure the motion of stars and galaxies.

5. Can the Doppler effect be observed with all types of waves?

Yes, the Doppler effect can be observed with all types of waves, including sound waves, light waves, and even water waves. It is a fundamental principle of wave behavior and can be observed in a wide range of natural phenomena.

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